Abstract
The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author
| Original language | English |
|---|---|
| Pages (from-to) | 129-167 |
| Number of pages | 39 |
| Journal | Geophysical and Astrophysical Fluid Dynamics |
| Volume | 16 |
| Issue number | 1-2 |
| Publication status | Published - 1980 |
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ASJC Scopus subject areas
- Geochemistry and Petrology
- Geophysics
- Space and Planetary Science
- Computational Mechanics
- Mechanics of Materials
- Astronomy and Astrophysics
Cite this
On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case. / Eltayeb, I. A.
In: Geophysical and Astrophysical Fluid Dynamics, Vol. 16, No. 1-2, 1980, p. 129-167.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.
AU - Eltayeb, I. A.
PY - 1980
Y1 - 1980
N2 - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author
AB - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author
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M3 - Article
VL - 16
SP - 129
EP - 167
JO - Geophysical and Astrophysical Fluid Dynamics
JF - Geophysical and Astrophysical Fluid Dynamics
SN - 0309-1929
IS - 1-2
ER -